Our primary long-term objective is development and application of methods for relating function, design, and significance of integrated biological systems to their underlying molecular determinants. As a result of the molecular advances in the past few decades, we are now in a position to examine the integrated behavior from an informed molecular perspective. This proposal is concerned with five specific aims; namely, (1) analysis of a new class of linked gene circuits for the regulation of inducible systems, (2) analysis of analogous linked gene circuits for the regulation of repressible systems, (3) analysis of accessory elements in the control of transcription termination and their influence on the dynamics of regulation, (4) analysis of symmetrical regulatory mechanisms governing amphibolic processes, and (5) development of canonical nonlinear methods for efficient simulation of biological processes. The methodology emphasized in our approach is mathematical and computer- assisted analysis because of their unique ability to systematically relate integrated function and design of organizationally complex biological systems to their molecular elements. The general outline for the analysis in each case is as follows: Specific models based on known or suspected molecular elements and interactions are formulated; the integrated behavior of these models is analyzed and compared according to several different criteria for functional effectiveness; the results of the analysis are interpreted in terms of optimal designs for specific functions; and, finally, the biological significance of the results is addressed and predictions are made for experimental testing. The projects of this proposal are likely to contribute to our understanding of normal processes such as homeostasis, growth and development, and of pathological manifestations such as metabolic diseases, developmental abnormalities and cancer.